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Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle

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    SYSNO ASEP0575046
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleReverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle
    Author(s) Krejčiřík, D. (CZ)
    Lotoreichik, Vladimir (UJF-V) ORCID, SAI
    Vu, T. (CZ)
    Number of authors3
    Article number63
    Source TitleApplied Mathematics and Optimization. - : Springer - ISSN 0095-4616
    Roč. 88, č. 2 (2023)
    Number of pages33 s.
    Publication formPrint - P
    Languageeng - English
    CountryUS - United States
    KeywordsRobin Laplacian ; Lowest eigenvalue ; Spectral optimisation ; Triangles
    OECD categoryApplied mathematics
    R&D ProjectsGA21-07129S GA ČR - Czech Science Foundation (CSF)
    Method of publishingOpen access
    Institutional supportUJF-V - RVO:61389005
    UT WOS001049245900003
    EID SCOPUS85168304684
    DOI10.1007/s00245-023-10033-1
    AnnotationWe consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter.
    WorkplaceNuclear Physics Institute
    ContactMarkéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228
    Year of Publishing2024
    Electronic addresshttps://doi.org/10.1007/s00245-023-10033-1
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